According to The Sun, the unnamed girl at the private Altrincham Grammar School (above) taunted fellow pupils as she videoed the stunt using social media app Snapchat.
The newspaper says the video went viral on Snapchat but, given that pictures and videos disappear permanently after a few seconds on the app, it's now unretrievable.
It was captioned "good bye(ble)".
Altrincham Grammar School warned the girl over her actions and informed her parents but did not enforce any other punishment.
One relative of a pupil at the school told the paper: "It is disgusting to think this young girl thinks it's acceptable to insult a religion by defacing a Bible like this.
"If a Christian pupil did this to a Koran, there would be uproar.
"I think the school should have made a bigger response. She was let off with just a warning but I think it's a lot more serious than that."
A spokesman for the school said: "This was an isolated incident, we dealt with it privately and immediately.
"The child has apologised."
